An open rectangular tank of dimensions `6mxx5mxx4m` contains water upto height of 2m. The vessel is accelerated horizontally with an acceleration of `am//s^(2)` as shown. Take `rho_("water")=10^(3)kg//m^(3)`
`g=10m//s^(2)` atmospheric pressure `=10^(5)N//m^(2)`. Bese on above information answer the following questions:
Determine the maximum value of a so that no water comes out from tan k.

Options

A. `g`
B. `(2g)/(3)`
C. `(g)/(3)`
D. `2g`

Answer

B

Explanation

The angle made by free surface of liquid with horizontal is `theta=tan^(-1)((a)/(g))`
For no water to spill out, limiting case is shown in the fig. As volume of water inside the beaker remains the same to,
`2xx6xx5=(1)/(2)(4+y)xx6xx5impliesy=0`
`tantheta=(4-y)/(6)=(2)/(3)=(a)/(g)impliesa=(2g)/(3)`